Probability logics. (English) Zbl 1224.03005

Ognjanović, Zoran; Rašković, Miodrag; Marković Zoran

Ognjanović, Zoran (ed.), Logic in computer science. Beograd: Matematički Institut SANU (ISBN 978-86-80593-40-1/pbk). Zbornik Radova (Beograd) 12(20), 35-111 (2009).

This is a precious, extensive overview of results regarding the logical systems dealing with uncertain reasoning. The authors present a number of probability logics, their axiomatization, completeness, compactness and decidability, followed by useful comments on possible applications. The cases of propositional and predicate languages extended by probability operators are covered, but also the probabilistic variants of nonclassical logics. The paper summarizes the historical development of this area as well.
For the entire collection see [Zbl 1158.00015].

Reviewer: Branislav Boričić (Beograd)

MSC:

03B48	Probability and inductive logic
03B60	Other nonclassical logic
68T27	Logic in artificial intelligence
68T37	Reasoning under uncertainty in the context of artificial intelligence

Keywords:

survey paper; conditional probability; approximate probability; nonstandard analysis; strong completeness; decidability; default reasoning